Open Problems

These are open problems that I've encountered in the course of my
research. Not surprisingly, almost all the problems are
geometric in nature. A name in brackets is
the first person to describe the problem to me; this may not be
original source of the problem. If there's no name, either I thought
of the problem myself (although I was certainly not the first to do
so), or I just forgot who told me.

Problems in bold are described in more detail than the others,
and are probably easier to understand without a lot of background
knowledge.

If you have any ideas about how to solve these problems, or if you
have any interesting open problems you'd like me to add, please let me know. I'd love to
hear them!

Caveat lector!

This web page and its children have not been significantly updated since 2001. Many of the problems listed on this page have been partially or even completely solved since then. Please do not cite these pages as evidence that a problem is still open; that makes no more sense than citing a paper published in 2001!

Recommended Books

Old and New Unsolved Problems in Plane Geometry and Number Theory by
Victor Klee and
Stan Wagon (MAA, 1991).

We should try to love the questions themselves, like locked rooms
and like books that are written in a very foreign tongue.

- Rainer Maria Rilke

Problem solving is hunting. It is savage pleasure, and we are born
to it.

- Thomas Harris, The Silence of the Lambs

If you keep proving stuff that others have done, getting confidence,
increasing the complexities of your solutions - for the fun of it -
then one day you'll turn around and discover that nobody actually
did that one! And that's the way to become a computer scientist.